(5p+1)(p+4)=2(7p+5)

Solution for (5p+1)(p+4)=2(7p+5) equation:

Simplifying
(5p + 1)(p + 4) = 2(7p + 5)

Reorder the terms:
(1 + 5p)(p + 4) = 2(7p + 5)

Reorder the terms:
(1 + 5p)(4 + p) = 2(7p + 5)

Multiply (1 + 5p) * (4 + p)
(1(4 + p) + 5p * (4 + p)) = 2(7p + 5)
((4 * 1 + p * 1) + 5p * (4 + p)) = 2(7p + 5)
((4 + 1p) + 5p * (4 + p)) = 2(7p + 5)
(4 + 1p + (4 * 5p + p * 5p)) = 2(7p + 5)
(4 + 1p + (20p + 5p2)) = 2(7p + 5)

Combine like terms: 1p + 20p = 21p
(4 + 21p + 5p2) = 2(7p + 5)

Reorder the terms:
4 + 21p + 5p2 = 2(5 + 7p)
4 + 21p + 5p2 = (5 * 2 + 7p * 2)
4 + 21p + 5p2 = (10 + 14p)

Solving
4 + 21p + 5p2 = 10 + 14p

Solving for variable 'p'.

Reorder the terms:
4 + -10 + 21p + -14p + 5p2 = 10 + 14p + -10 + -14p

Combine like terms: 4 + -10 = -6
-6 + 21p + -14p + 5p2 = 10 + 14p + -10 + -14p

Combine like terms: 21p + -14p = 7p
-6 + 7p + 5p2 = 10 + 14p + -10 + -14p

Reorder the terms:
-6 + 7p + 5p2 = 10 + -10 + 14p + -14p

Combine like terms: 10 + -10 = 0
-6 + 7p + 5p2 = 0 + 14p + -14p
-6 + 7p + 5p2 = 14p + -14p

Combine like terms: 14p + -14p = 0
-6 + 7p + 5p2 = 0

Factor a trinomial.
(-2 + -1p)(3 + -5p) = 0

Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve:

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
Set the factor '(3 + -5p)' equal to zero and attempt to solve:

Simplifying
3 + -5p = 0

Solving
3 + -5p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -5p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5p = 0 + -3
-5p = 0 + -3

Combine like terms: 0 + -3 = -3
-5p = -3

Divide each side by '-5'.
p = 0.6

Simplifying
p = 0.6
Solution
p = {-2, 0.6}